Measure causal impact of YouTube ads

Estimate the incremental effect of a 6‑week YouTube campaign on weekly online sales.

• Explain why naive OLS of sales on ad spend is biased; list at least three confounders (e.g., seasonality, promotions, targeting) and the likely direction of bias.
• Propose a primary design (geo‑level randomized controlled trial or matched‑market test) and a backup quasi‑experiment (difference‑in‑differences or synthetic control). State identification assumptions and diagnostics.
• Incorporate ad‑stock/lagged effects (e.g., Koyck/geometric decay) and define the estimand: incremental ROAS over and post campaign.
• Compute required sample size for a geo‑experiment given baseline weekly sales μ=100,000, coefficient of variation=0.25, minimal detectable effect=3%, α=0.05, power=0.8; show formulas and approximate number of geos per arm.
• Detail pre‑trend checks, spillover/interference detection, and how you will aggregate heterogeneous treatment effects (by geo size, baseline sales, or audience overlap).